The diaphragm vibrato has nothing to do with the diaphragm. It is possible to get the air supply to oscillate causing vibrato - that is body tension, abs not the diaphragm.
The tongue is used by singers too Taah-eeh-aah like stchasking said.
Moving the jaw up and down is yet another way
Finally shaking the horn.
Our playing is always the sum of our virtues and deficits. We practice to reduce the deficits and add to the virtues. Once we have developed habits, it is tough to break them, that is why some of us have problems with different concepts. It makes sense to work on vibrato in all its forms. It is an easy, low time investment way to increase expression.